Mahmud Zakut, 20, was killed in Beit Hanun in an area near the border fence with Israel, emergency services spokesman Adham Abu Selmiya said in a statement sent to AFP.
Witnesses said the injuries occurred when dozens of young men went to the northern border in spite of attempts by Hamas police to stop them from approaching the area.
The statement said a total of 37 people had been wounded by gunfire throughout the afternoon demonstrations in Gaza, most of them in the Beit Hanun area.
At least six people were wounded near the border close to the southern town of Khan Yunis, Abu Selmiya said earlier.
Another 281 people were injured during a raft of demonstrations in the West Bank and east Jerusalem throughout the day, 14 of whom were hit by rubber bullets, medics said. (*)